Question: Divide the polynomials.
Solution: Usually, there are many different ways to divide polynomials. Here, we will use the method of splitting the quotient into multiple quotients: $\dfrac{3x^3-x-2}{x}=\dfrac{3x^3}{x}-\dfrac{x}{x}-\dfrac{2}{x}$ Now let's try to cancel common factors in the resulting terms. $\begin{aligned} \dfrac{3x^3}{x}&=3x^2 \\\\ -\dfrac{x}{x}&=-1 \end{aligned}$ $-\dfrac{2}{x}$ doesn't have common factors so it has to stay as it is. In conclusion, this is the result of dividing the polynomials: $3x^2-1-\dfrac{2}{x}$ [I want to see a different way of performing the division.]